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Write an expression to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n = 1$ for the first term. $\newline$ $\text{-}75, \text{-}150, \text{-}225, \text{-}300, \ldots$ $\newline$ $a_n =$ _____

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Write variable expressions for arithmetic sequences

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Q. Write an expression to describe the sequence below. Use

n

to represent the position of a term in the sequence, where

n = 1

for the first term.

\newline

\text{-}75, \text{-}150, \text{-}225, \text{-}300, \ldots

\newline

a_n =

_____

Sequence Type: We have: $\newline$ – $75$ , – $150$ , – $225$ , – $300$ , ... $\newline$ Is the given sequence geometric or arithmetic? $\newline$ – $75$ , – $150$ , – $225$ , – $300$ , ... $\newline$ Here, there is a common difference between consecutive terms. $\newline$ The given sequence is arithmetic.
Initial Values: $-75, -150, -225, -300, \ldots$ $\newline$ Determine the values of $a_{1}$ and $d$ of the sequence. $\newline$ The first term, $a_{1} = -75$ $\newline$ Common difference, $d = -150 - (-75) = -75$
Expression Formulation: We have: $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_1 = -75$ $\newline$ $d = -75$ $\newline$ Write an expression to describe $-75, -150, -225, -300, \ldots$ $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_n = -75 + (n-1) \times (-75)$ $\newline$ $a_n = -75 - 75n + 75$ $\newline$ $a_n = -75n$

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